Reading Algebraic Expressions

Reading algebraic expressions can be confusing for some. Use this lesson on reading algebraic equations to help you better understand them.

Introduction

If you're new to algebra—or haven't thought about it in a while—one of the first things you might notice is that algebra problems look a bit different from simple arithmetic problems. Take the expression below, for instance:

x + 4x ⋅ 22 - ( 3 / x )

It's not that difficult to solve once you know how to do it, but it does include a few symbols that are common in algebra but not in more basic math. The way you write algebra expressions is called algebraic notation. While it might look tricky at first, algebraic notation isn't that complicated.

Algebraic notation includes five main components: variables, coefficients, operators, exponents, and parentheses. You can see all five of them in the expression below:

We'll go through these one by one.

Variables

A variable is a letter that is used to represent a number. For instance, in this problem the variable x represents an unknown number that will equal 5 when added to 2.

2 + x = 5

In other words, this expression is asking the question, "What number can you add to 2 to get 5?" We wrote x because we didn't know what the number was at first—but we can figure it out. Since we know that 2 + 3 = 5, our variable must be equal to 3. In other words, x = 3.

Although this was a simple addition problem, the fact that it included a variable made it an algebra problem. In fact, finding the value of an unknown number is often the goal in algebra.

While x is the most commonly used variable, any letter can be a variable. An algebra problem can have one variable or many. If a variable is used more than once in the same problem, it's equal to the same number each time. Take this equation:

x + x + y = 20

Each x in this expression is equal to the same amount. The other variable, y, may be equal to a different amount.

Just because you find the value for a variable in one problem doesn't mean the variable will have the same value in a different problem. For instance, while x was equal to 3 in our first problem, it isn't necessarily equal to 3 in any other expression.

Coefficients

Sometimes you'll see a variable with another number in front of it, like this:

2x

In this example, 2 is the coefficient. Coefficients are a way to group variables. For example, 2x is just another way to write x + x. Could you use coefficients to rewrite this expression?

x + x + x + x + y + y + y

Because there are four xs and three ys, you could write this as 4x + 3y. Without knowing what x and y are equal to, we can't simplify it even further—but it is a lot simpler to read:

4x + 3y

You may be wondering why we can't simplify this even further to 7xy. This is because you can only add or subtract variables that are the same—so you can add x + x or y + y but neverx + y. For more information about adding and subtracting variables, check out our Simplifying Expressions lesson.